The damage formula is important to understand once you have completed your first weapon grid and find a new Omega SSR weapon or draw one during a Premium Gala. Based on what your current weapons are and what summons you have available to you, what ultimately increases your damage and overall strength will depend.
This article is merely a rehashing of information commonly referenced on ProBoards and reddit. Please refer to the relevant topics for detailed information:
- Weapon / Summon Optimization and Progression (ProBoards)
- Damage Calculations Explained (reddit)
How does the damage formula affect me?[]
The main reason the formula is important is because the only in-game indication of your overall strength level is your main character's ATK value in the Party screen. This value is simply the sum of all your weapons' ATK values, plus the weapon proficiency bonus, which is an increased 20% from each weapon that your current class can equip. This value does not factor in the skills and skill levels of your weapons, nor does it account for your main summon or what support summon you choose. This means that it is unclear whether to use Ifrit or Colossus Omega as your main summon, and what you should pick as your support summon to complement it.
So what is the damage formula?[]
In very simple terms, the formula is as follows:
Overall power = ATK * Boost%
Boost% = Normal boost * Omega boost * Unknown boost * Elemental boost
What's the difference between all the boost types?[]
This is where things get kind of complicated.
Elemental[]
First, Elemental boost is the simplest to explain. If your element is strong against the enemy's element, your Elemental boost is 50%. In addition to this, if your summon says "X% boost to [element] ATK," then it is also an Elemental boost. Most summons are Elemental, but there are exceptions that are not. The key is to look at the Aura; if instead it said "X% boost to [element] allies' ATK," then this is instead commonly known as a Character Summon and it counts as part of your Normal boost. If both summons you use in battle are Elemental, and you have the elemental advantage, you would add both summons together plus 50%. For example, if you use a 4★ Ifrit and also a friend's 4★ Ifrit against a Wind raid boss, your Elemental boost is going to be 60% + 60% + 50% = +170% = 270%.
Omega[]
Next, Omega boost looks at every weapon that comes from a primal beast raid, namely Tiamat, Colossus, Leviathan, Yggdrasil, Luminiera, and Celeste. All of the skills on these weapons, if you look at the status screen, have an M in the top left of the icon. This denotes it a "Magna" skill (the Japanese name for Omega), which means the skill increases your Omega boost. Only ATK skills matter, and the way they work is as follows:
- Small boosts have a base of 0%
- Medium boosts have a base of 2%
- Large/Big boosts have a base of 5%
- Every skill level is worth 1% per level, up to level 10
- For skill level 11 and higher, each level is worth less than 1%. This will be covered later.
- For unfinished Bahamut Weapons that boost 2 races, each level is worth 0.5% instead.
So, if you have 5 Colossus Cane Omega (big) and 5 Colossus Breaker (medium), all at skill level 1, your Omega boost would be 5*6% + 5*3% = +45% = 145%. If they are all skill level 2, your boost becomes 155%. The last piece to the Omega boost is the Omega summon. Colossus Omega reads "50% boost to Vulcan's skills," which is kind of vague and unhelpful. Once again, look at the status screen for one of your Omega weapons; Colossus Cane Omega's Aura is named Vulcan's Might II - in other words, the Colossus Omega summon increases the boost value of Colossus Cane Omega by 50%. All of your Colossus weapons have skills named Vulcan's, so they would all be increased. So using the previous example, if you have 5 Canes and 5 Breakers all at skill level 2, your initial Omega boost is going to be +55%. If you were to use 2 Colossus Omega summons, 50% each, that boost would become +110% = 210%.
Normal[]
Next, Normal boost is pretty much the opposite of Omega boost: continuing to use the Fire element as an example, it looks for weapons with the skill names Fire's, Hellfire's, or Inferno's in the skill name, which, once again, can be found on the weapon's status screen. Normal weapon skills do not have any letters in the top left of the skill icon. If you understand how the Omega boost works, this should be easy, since it works exactly the same way. So if you've been super busy farming Ifrit Showdown, maybe you have 1 Ifrit Halberd (big), 3 Ifrit Blades, 3 Ifrit Daggers, and 3 Ifrit Axes (all medium), all at skill level 2. Your Normal boost would be 6+1% + 3*(3+1)% + 3*(3+1)% + 3*(3+1)% = +43% = 143%. Same as Omega boost, there is also a summon that boosts only Normal skills, although it can only be obtained from a Premium Draw. For Fire, that summon is Agni, and his Aura reads similarly: "80% boost to Fire's, Hellfire's, and Inferno's skills."
There are also Normal II skills, denoted by the II in the top left of the icon. These skills are worth an additional 1% at every level, and can also be leveled up to skill level 15. Other than the difference in how much % it's worth, it is counted in the Normal boost as, well, normal.
Bahamut Weapons also fall into the Normal category
Unknown[]
Last, we have the Unknown boost. This one is really rather simple: any weapon skill that is not an Omega or Normal falls here. The easiest way to tell is, like Omega weapons, the skill icon in the status screen for Unknown weapon skills has a EX in the top left corner of the icon. Most of these weapons will come from collaboration events. Currently, only the Ranko Kanzaki summon (connected to the IDOLM@STER: Cinderella Girls collaboration events) has an Aura that boosts Unknown weapons, and she specifically boosts Mysterious skills, which only weapons from IM@S:CG events have. For example, the weapons from the A Tale of Intersecting Fates event have Unknown skills named "Strength" that are not affected by Ranko Kanzaki.
Again, the calculations are the same as for Omega and Normal boosts, check the Big/Medium/Small adjective in the skill description, add 1% per skill level.
OK, now that I understand the types of boosts, how do I apply it?[]
Glad you asked! Let's make up a weapon grid: for the sake of variety, we will use Ray of Zhuque from Rise of the Beasts (it becomes Normal II at level 100, but we will assume it is not Normal II yet), 3 Colossus Cane Omegas, 3 
Colossus Breakers, a Balanced Blade from A Tale of Intersecting Fates, and 2 Ifrit Blades. Let's say everything is skill level 5. So first, we separate the boosts into their respective categores.
- Normal
- Ray of Zhuque (Big) = 5% + 5%
- Ifrit Blade (Medium) = 2% + 5%
- Ifrit Blade (Medium) = 2% + 5%
- Omega
- Colossus Cane Omega (Big) = 5% + 5%
- Colossus Cane Omega (Big) = 5% + 5%
- Colossus Cane Omega (Big) = 5% + 5%
- Colossus Breaker (Medium) = 2% + 5%
- Colossus Breaker (Medium) = 2% + 5%
- Colossus Breaker (Medium) = 2% + 5%
- Unknown
- Balanced Blade (Big) = 5% + 5%
- Elemental
- [none]
Add the values together and we have Normal boost = 124%, Omega boost = 151%, Unknown = 110%, Elemental = 100%. So, from weapons alone, the boost is:
124% * 151% * 110% * 100% = 205.96%
However, usually the question being asked is "which summon should I be using?", and the choices are usually between an Elemental summon and an Omega summon. So let's do the math for the common Fire options:
- Ifrit 0★: Elemental +40%
- Ifrit 4★: Elemental +60%
- Colossus Omega 0★: Omega boost * 50%
- Colossus Omega 3★: Omega boost * 100%
For those who don't enjoy math, this really is the point you care about. So, with these summon options, we'll construct a table to display every combination of summons.
| Ifrit 0★ | Ifrit 4★ | Colossus Ω 0★ | Colossus Ω 3★ | |
|---|---|---|---|---|
| Ifrit 0★ | 124%*151%*110%*180%=370.73% | 124%*151%*110%*200%=411.93% | 124%*176.5%*110%*140%=337% | 124%*202%*110%*140%=385.73% |
| Ifrit 4★ | 124%*151%*110%*200%=411.93% | 124%*151%*110%*220%=453.12% | 124%*176.5%*110%*160%=385.19% | 124%*202%*110%*160%=440.84% |
| Colossus Ω 0★ | 124%*176.5%*110%*140%=337% | 124%*176.5%*110%*160%=385.19% | 124%*202%*110%*100%=275.53% | 124%*228.5%*110%*100%=311.67% |
| Colossus Ω 3★ | 124%*202%*110%*140%=385.73% | 124%*202%*110%*160%=440.84% | 124%*228.5%*110%*100%=311.67% | 124%*253%*110%*100%=345.09% |
So, as you can see, using 2 Ifrit 4★ gives you the most boost with this exact weapon pool. However, knowing this information is still good for when you don't have all summon options. If you only have Colossus Omega 0★, you can still see that Ifrit 4★ will be the best support summon to choose, followed by Ifrit 0★, then Colossus Omega 3★.
My head hurts. In other words, does this mean I should make Ifrit 4★ and always pick him?[]
Well, not exactly. While you will want your own 4★ summon because they're good in general, there is a point where using Colossus Omega 3★ and Ifrit 4★ will be better than using 2 Ifrit 4★. Since Normal and Unknown weapons are staying the same, we can remove them from the formula to avoid mistakes, but here is the formula:
(100% + Omega * 200%) * (100% + 60%) = (100% + Omega) * (100% + 120%)
Colossus Omega 3★ doubles your Omega modifier, so that's Omega * 200%. Each Ifrit 4★ boosts by 60%, so on the left we have a single Ifrit, while on the right we combined two Ifrit boosts. Now, here is the algebra proof:
(1 + 2 Omega) * 1.6 = (1 + Omega) * 2.2
1.6 + 3.2 Omega = 2.2 + 2.2 Omega
(3.2 - 2.2) Omega = 2.2 - 1.6
Omega = .6 = 60%
In other words, when you have exactly +60% boost from Omega weapons, Ifrit 4★ and Colossus Omega 3★ are exactly equal in strength. If you have over +60% Omega weapon boost, then using one Colossus Omega 3★ will be superior to using 2 Ifrit 4★. Also keep in mind that if, for example, you have a lot of Athena 3/4★ friends, her higher elemental boost of +80% means you need less Omega skill before Colossus Omega 3★ becomes better than Ifrit.
This is a chart listing the most common summon multipliers. Find your own elemental summon down the left side, then your support/friend summon along the top. Where the two meet is the Omega skill you need to use a fully uncapped Omega summon over your existing elemental summon.
Parting Words[]
Again, this information is readily available at many other places, and the two posts linked at the top of this article will go into more detail. However, this should at least serve as an introduction into Granblue Fantasy math and theorycrafting, and help you understand the impact of your weapon grid and summon choices.